Finite Group Databasebeta

← #25098006

Subgroups — #25098006

Order 11008.

1766 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063354C211yesmaximal, characteristic
2C2×#14583378C211yesmaximal, characteristic
3C2×#14582892C211yesmaximal, characteristic
4C2×#103×D43C211yesmaximal, characteristic, complemented
5#19137178C211yesmaximal, characteristic, complemented
6#19134939C211yesmaximal, characteristic, complemented
7#19134937C211yesmaximal, characteristic, complemented
8#19134935C211yesmaximal, characteristic, complemented
9#19134933C211yesmaximal, characteristic, complemented
10#19134931C211yesmaximal, characteristic, complemented
11#19134929C211yesmaximal, characteristic, complemented
12#19134927C211yesmaximal, characteristic, complemented
13#19134313C211yesmaximal, characteristic, complemented
14#19134290C211yesmaximal, characteristic, complemented
15C43×#1877C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×Q8×D43C2211yescharacteristic
18C2×#13063354—24no—
19C2×#13063354—24no—
20C2×#13063354C418yescomplemented
21C22×Dic172C2211yescharacteristic
22C22×#10621885C2211yescharacteristic
23C22×#10621883C2211yescharacteristic
24C22×#10621872C2211yescharacteristic
25C22×C8×D43C2211yescharacteristic
26#14583378—24no—
27#14583378—24no—
28C2×C4×Dic86C2211yescharacteristic
29C2×#13063290C2211yescharacteristic
30C2×D4×Dic43C2211yescharacteristic
31C2×C4×C22⋊D43—21no—
32C2×(C22⋊D43)⋊C4—21no—
33C2×#13063283C2211yescharacteristic
34C2×#13063282C2211yescharacteristic
35C2×#13063281—21no—
36C22×Dic43⋊C4—21no—
37C2×C4⋊C4×D43C2211yescharacteristic
38#14582892—24no—
39C2×#13063250C2211yescharacteristic
40C2×#13063250C2211yescharacteristic
41C2×#13063249C2211yescharacteristic
42C2×#13063248C2211yescharacteristic
43C2×#13063248C2211yescharacteristic
44#103×D43—24no—
45C2×#13063246C2211yescharacteristic
46#14582806C2211yescharacteristic
47#14582805C2211yescharacteristic
48#14582804C2211yescharacteristic
49#14582803—21no—
50#14582803—21no—
51#14582761—21no—
52#14582761—21no—
53#14582662C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56#14582654C2211yescharacteristic
57#14582653C2211yescharacteristic
58#14582653C2211yescharacteristic
59C22×SD16×C43C2211yescharacteristic
60C2×C4×D4×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C43×#391C2211yescharacteristic
64C43×#340C2211yescharacteristic
65C43×#336C2211yescharacteristic
66C2×#10621900—22no—
67C2×#10621900—22no—
68C2×#10621900—22no—
69C2×#10621900C2×C414yes—
70C2×#10621900D414yes—
71C2×#10621900D414yes—
72C22×Dic86—21no—
73C22×Dic86C2311yescharacteristic
74C22×Dic86C2311yescharacteristic
75C2×Q8×D43—22no—
76C2×Q8×D43—22no—
77C2×Q8×D43—22no—
78C2×Q8×D43—22no—
79C2×Q8×D43—22no—
80C2×Q8×D43C2×C414yescomplemented
81C22×C22⋊D43—21no—
82C23×Dic43—21no—
83C23×Dic43—21no—
84C22×C4×D43—21no—
85C22×C4×D43—21no—
86C22×C4×D43C2311yescharacteristic
87#13063354—232no—
88C2×Dic172—22no—
89C2×Dic172—22no—
90C2×Dic172C2×C414yescomplemented
91C2×#10621885—22no—
92C2×#10621885—22no—
93C2×#10621885C2×C414yescomplemented
94C2×#10621883—22no—
95C2×#10621883—22no—
96C2×#10621883C2×C414yescomplemented
97C2×#10621872—22no—
98C2×#10621872—22no—
99C2×#10621872C2×C414yescomplemented
100C22×C43⋊C8C2311yescharacteristic
101C22×C43⋊C8C2311yescharacteristic
102C2×C8×D43—22no—
103C2×C8×D43—22no—
104C2×C8×D43—22no—
105C4×Dic86—22no—
106C4×Dic86—22no—
107#13063290—22no—
108#13063290—22no—
109D4×Dic43—22no—
110D4×Dic43—22no—
111C4×C22⋊D43—28no—
112(C22⋊D43)⋊C4—28no—
113#13063283—22no—
114#13063283—22no—
115#13063282—22no—
116#13063282—22no—
117#13063281—28no—
118C2×C4⋊Dic43C2311yescharacteristic
119C2×C4⋊Dic43C2311yescharacteristic
120C2×Dic43⋊C4—28no—
121C2×Dic43⋊C4—21no—
122C2×Dic43⋊C4—21no—
123C2×Dic43⋊C4—21no—
124C2×Dic43⋊C4D411yescharacteristic
125C2×Dic43⋊C4D411yescharacteristic
126C4⋊C4×D43—22no—
127C4⋊C4×D43D414yes—
128C2×C22⋊Dic43—21no—
129C2×(C2×D43)⋊C4—21no—
130C2×(C2×D43)⋊C4D411yescharacteristic
131C2×(C2×D43)⋊C4D411yescharacteristic
132C2×C4×Dic43—21no—
133C2×C4×Dic43—21no—
134C2×C4×Dic43—21no—
135C2×C4×Dic43C2311yescharacteristic
136#13063250—22no—
137#13063250—22no—
138#13063249—22no—
139#13063248—22no—
140#13063248—22no—
141#13063246—22no—
142C43⋊#95—21no—
143C43⋊#95—21no—
144C43⋊#95—21no—
145C43⋊#95—21no—
146C43⋊#95—21no—
147C43⋊#95—21no—
148C22×Q8×C43C2311yescharacteristic
149C22×D4×C43C2311yescharacteristic
150C23×C4×C43—21no—
151C2×SD16×C43—22no—
152C2×SD16×C43—22no—
153C2×SD16×C43C2×C414yescomplemented
154C22×C8×C43C2311yescharacteristic
155C22×C8×C43C2311yescharacteristic
156C4×D4×C43—22no—
157C4×D4×C43—22no—
158C2×C4⋊C4×C43C2311yescharacteristic
159C2×C4⋊C4×C43C2311yescharacteristic
160C2×C22⋊C4×C43—21no—
161C2×C42×C43C2311yescharacteristic
162#103×C43—22no—
163#102×C43—22no—
164#95×C43—21no—
165#95×C43—21no—
166C24×C43—21no—
167C23×D43C2×D411yescharacteristic
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43C22×C412yes—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43C22×C412yes—
178C2×D4×C43C2×D412yes—
179C2×D4×C43C2×D412yes—
180C22×C4×C43—24no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—81no—
185C22×C4×C43—81no—
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2411yescharacteristic
189C2×C22⋊D43—24no—
190C2×C22⋊D43—24no—
191C2×C22⋊D43—24no—
192C22×Dic43—24no—
193C22×Dic43—24no—
194C22×Dic43—24no—
195C22×Dic43—24no—
196C22×Dic43—21no—
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—81no—
201C22×Dic43—81no—
202C22×Dic43C2×D411yescharacteristic
203C22×Dic43C2×D411yescharacteristic
204C22×Dic43C2×D411yescharacteristic
205Q8×D43—28no—
206Q8×D43—28no—
207Q8×D43—44no—
208Q8×D43—44no—
209#10621900—28no—
210#10621900—28no—
211#10621900—28no—
212#10621900C22⋊C4116yes—
213C2×C4×D43—24no—
214C2×C4×D43—24no—
215C2×C4×D43—42no—
216C2×C4×D43—42no—
217C2×C4×D43—81no—
218C2×C4×D43—81no—
219C2×C4×D43C22×C412yes—
220C2×C4×D43C2×D412yes—
221C2×C4×D43C2×D412yes—
222C2×C4×D43C2×D412yes—
223C2×C4×D43#4112yes—
224C2×C4×D43#4112yes—
225C2×Dic86—21no—
226C2×Dic86—21no—
227C2×Dic86—21no—
228C2×Dic86—21no—
229C2×Dic86—21no—
230C2×Dic86—21no—
231C2×Dic86—21no—
232C2×Dic86—21no—
233C2×Dic86—24no—
234C2×Dic86—42no—
235C2×Dic86—42no—
236C2×Dic86C22×C412yes—
237C2×Dic86C22×C412yes—
238C2×Dic86C2×D412yes—
239C2×Dic86C2×D412yes—
240SD16×C43—28no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43C22×C412yes—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43C2×D412yes—
251C22⋊C4×C43—24no—
252C42×C43—21no—
253C42×C43—21no—
254C22⋊Dic43—24no—
255#10621885—28no—
256#10621883—28no—
257(C2×D43)⋊C4—22no—
258(C2×D43)⋊C4—22no—
259(C2×D43)⋊C4—42no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43C2×D412yes—
264Dic43⋊C4—24no—
265Dic43⋊C4—24no—
266Dic43⋊C4—24no—
267Dic43⋊C4—22no—
268Dic43⋊C4—22no—
269C4×Dic43—24no—
270C4×Dic43—24no—
271C4×Dic43—21no—
272C4×Dic43—21no—
273C4×Dic43—42no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8C22×C412yes—
280Dic172—28no—
281#10621872—28no—
282C8×D43—44no—
283C23×C43—22no—
284C23×C43—22no—
285C23×C43—22no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43C22×D411yescharacteristic
291C22×D43—21no—
292C22×D43—21no—
293C22×D43—21no—
294C22×D43—21no—
295C22×D43C4×D412yes—
296C22×D43#12012yes—
297C22×D43#12112yes—
298Q8×C43—22no—
299Q8×C43—22no—
300Q8×C43—41no—
301Q8×C43—41no—
302D4×C43—22no—
303D4×C43—22no—
304D4×C43—22no—
305D4×C43C2×C22⋊C414yes—
306C2×C4×C43—22no—
307C2×C4×C43—21no—
308C2×C4×C43—22no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—84no—
322C2×C4×C43C23×C411yescharacteristic
323C2×C4×C43C22×D411yescharacteristic
324C2×C4×C43C22×D411yescharacteristic
325C2×C4×C43C22×D411yescharacteristic
326C2×C4×C43C2×#4111yescharacteristic
327C2×C4×C43C2×#4111yescharacteristic
328C22⋊D43—216no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—216no—
333C2×Dic43—22no—
334C2×Dic43—21no—
335C2×Dic43—21no—
336C2×Dic43—22no—
337C2×Dic43—21no—
338C2×Dic43—21no—
339C2×Dic43—21no—
340C2×Dic43—21no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43—84no—
349C2×Dic43C4×D412yes—
350C2×Dic43#12012yes—
351C2×Dic43#12112yes—
352C4×D43—48no—
353C4×D43—84no—
354C4×D43C2×C22⋊C414yes—
355C4×D43C4×D414yes—
356C4×D43#12114yes—
357C4×D43#12314yes—
358Dic86—22no—
359Dic86—22no—
360Dic86—22no—
361Dic86—22no—
362Dic86—22no—
363Dic86—41no—
364Dic86—41no—
365Dic86—48no—
366Dic86C2×C22⋊C414yes—
367C8×C43—22no—
368C8×C43—41no—
369C43⋊C8—22no—
370C43⋊C8—41no—
371#20931—431nomaximal, Sylow
372C22×C43—24no—
373C22×C43—42no—
374C22×C43—42no—
375C22×C43—42no—
376C22×C43—42no—
377C22×C43—42no—
378C22×C43—42no—
379C22×C43C2×C4×D411yescharacteristic
380C22×C43C2×#12011yescharacteristic
381C22×C43C2×#12111yescharacteristic
382C22×C43#57711yescharacteristic
383C22×C43#57711yescharacteristic
384C22×C43#57811yescharacteristic
385C22×C43#57811yescharacteristic
386C2×D43—22no—
387C2×D43—22no—
388C2×D43—22no—
389C2×D43—22no—
390C2×D43—22no—
391C2×D43—22no—
392C2×D43#38614yes—
393C4×C43—42no—
394C4×C43—41no—
395C4×C43—41no—
396C4×C43—42no—
397C4×C43—81no—
398C4×C43C22×C22⋊C411yescharacteristic
399C4×C43C2×C4×D411yescharacteristic
400C4×C43C2×#12111yescharacteristic
401C4×C43C2×#12311yescharacteristic
402Dic43—24no—
403Dic43—42no—
404Dic43—41no—
405Dic43—41no—
406Dic43—42no—
407Dic43—81no—
408Dic43#38614yes—
409C22×#137—431no—
410C2×#520—431no—
411C2×#416—431no—
412C22×#103—431no—
413#2310—431no—
414#1878—431no—
415#1878—431no—
416#1878—431no—
417#1878—431no—
418#1877—431no—
419#1877—431no—
420#1877—431no—
421#1877D4311yescharacteristic, complemented
422#1736—431no—
423#1729—431no—
424C2×C43—44no—
425C2×C43C2×#38611yescharacteristic
426C2×C43#294711yescharacteristic
427C2×C43#294711yescharacteristic
428C2×C43#300911yescharacteristic
429C2×C43#301111yescharacteristic
430C2×C43#304611yescharacteristic
431C2×C43#304611yescharacteristic
432D43—24no—
433C22×#41—431no—
434C23×Q8—431no—
435C2×#137—438no—
436C2×#137—864no—
437C2×#137—864no—
438C22×Q16—431no—
439C22×Q16—431no—
440C22×SD16—431no—
441C22×SD16C2×D4311yescharacteristic
442C22×M16—431no—
443C23×C8—431no—
444#520—864no—
445#520—864no—
446C2×C4×Q8—431no—
447C2×C4×Q8—431no—
448C2×C4×D4—431no—
449C2×C4×D4—861no—
450C2×C4×D4—861no—
451C2×C4×D4C2×D4311yescharacteristic
452C2×#117—431no—
453C2×#117—431no—
454C2×#117—861no—
455C22×C4⋊C4—431no—
456C22×C4⋊C4—861no—
457#416—864no—
458C2×#103—431no—
459C2×#103—431no—
460C2×#103—431no—
461C2×#103—431no—
462C2×#103—431no—
463C2×#103—864no—
464C2×#103C2×D4311yescharacteristic
465C2×#102—431no—
466C2×#102C2×D4311yescharacteristic
467#391—431no—
468#391—431no—
469#391—431no—
470#391—861no—
471#391—861no—
472#391C2×D4311yescharacteristic
473#381—861no—
474#381—861no—
475#340—431no—
476#340—431no—
477#340—431no—
478#340C2×D4311yescharacteristic
479#336—431no—
480#336—431no—
481#336—431no—
482#336C2×D4311yescharacteristic
483C43#2093111yescharacteristic, complemented, Sylow
484C2×#41—434no—
485C2×#41—434no—
486C2×#41—434no—
487C2×#41—862no—
488C2×#41—862no—
489C2×#41—862no—
490C22×Q8—434no—
491C22×Q8—431no—
492C22×Q8—431no—
493C22×Q8—861no—
494C22×Q8—862no—
495C22×Q8—862no—
496C22×Q8—862no—
497C22×Q8—862no—
498C22×Q8—862no—
499C22×Q8C22×D4311yescharacteristic
500C22×D4—861no—
501C22×D4C22×D4311yescharacteristic
502C23×C4—21no—
503C23×C4—431no—
504C23×C4—861no—
505C23×C4—861no—
506C23×C4—861no—
507C23×C4—861no—
508#137—8632no—
509C2×Q16—434no—
510C2×Q16—434no—
511C2×Q16—862no—
512C2×Q16—862no—
513C2×Q16—862no—
514C2×Q16—862no—
515C2×SD16—22no—
516C2×SD16—22no—
517C2×SD16—434no—
518C2×SD16—862no—
519C2×SD16—862no—
520C2×SD16C4×D4314yescomplemented
521C2×M16—434no—
522C2×M16—862no—
523C2×M16—862no—
524C22×C8—431no—
525C22×C8—431no—
526C22×C8—862no—
527C22×C8—862no—
528C22×C8—862no—
529C22×C8C22×D4311yescharacteristic
530C22×C8C22×D4311yescharacteristic
531C4×Q8—862no—
532C4×Q8—862no—
533C4×Q8—862no—
534C4×Q8—862no—
535C4×D4—22no—
536C4×D4—22no—
537C4×D4—868no—
538C4×D4—862no—
539C4×D4—868no—
540C4×D4—862no—
541#117—862no—
542#117—862no—
543#117—868no—
544#117—862no—
545#117—862no—
546C2×C4⋊C4—431no—
547C2×C4⋊C4—434no—
548C2×C4⋊C4—431no—
549C2×C4⋊C4—431no—
550C2×C4⋊C4—431no—
551C2×C4⋊C4—862no—
552C2×C4⋊C4—861no—
553C2×C4⋊C4—861no—
554C2×C4⋊C4—868no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4C22×D4311yescharacteristic
557C2×C4⋊C4C22×D4311yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—431no—
560C2×C22⋊C4—431no—
561C2×C22⋊C4—861no—
562C2×C22⋊C4—861no—
563C2×C42—431no—
564C2×C42—861no—
565C2×C42—861no—
566C2×C42—861no—
567C2×C42C22×D4311yescharacteristic
568#103—22no—
569#103—862no—
570#103—862no—
571#103—862no—
572#103—862no—
573#103—862no—
574#102—22no—
575#102—862no—
576#95—21no—
577#95—21no—
578#95—861no—
579#95—861no—
580#95—861no—
581#95—861no—
582#95—861no—
583#95—861no—
584C24—21no—
585C24—431no—
586#41—4316no—
587#41—868no—
588#41—868no—
589#41—868no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—432no—
596C2×Q8—432no—
597C2×Q8—432no—
598C2×Q8—432no—
599C2×Q8—864no—
600C2×Q8—868no—
601C2×Q8—868no—
602C2×Q8—861no—
603C2×Q8—861no—
604C2×Q8—861no—
605C2×Q8—861no—
606C2×Q8—861no—
607C2×Q8—861no—
608C2×Q8—861no—
609C2×Q8—861no—
610C2×Q8—1722no—
611C2×Q8—1722no—
612C2×Q8—1724no—
613C2×Q8—1724no—
614C2×Q8C2×C4×D4312yes—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—864no—
619C2×D4—864no—
620C2×D4—864no—
621C2×D4C2×C4×D4312yes—
622C2×D4D4×D4312yes—
623C2×D4D4×D4312yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—24no—
627C22×C4—21no—
628C22×C4—81no—
629C22×C4—81no—
630C22×C4—431no—
631C22×C4—432no—
632C22×C4—432no—
633C22×C4—432no—
634C22×C4—432no—
635C22×C4—432no—
636C22×C4—432no—
637C22×C4—431no—
638C22×C4—431no—
639C22×C4—864no—
640C22×C4—864no—
641C22×C4—864no—
642C22×C4—864no—
643C22×C4—864no—
644C22×C4—861no—
645C22×C4—864no—
646C22×C4—861no—
647C22×C4—861no—
648C22×C4—861no—
649C22×C4—3441no—
650C22×C4—3441no—
651C22×C4—3441no—
652C22×C4—3441no—
653C22×C4—1722no—
654C22×C4—1722no—
655C22×C4D4×D4311yescharacteristic
656C22×C4D4×D4311yescharacteristic
657C22×C4C23×D4311yescharacteristic
658Q16—868no—
659Q16—868no—
660SD16—28no—
661SD16—868no—
662M16—868no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—432no—
669C2×C8—861no—
670C2×C8—861no—
671C2×C8—861no—
672C2×C8—861no—
673C2×C8—861no—
674C2×C8—1724no—
675C2×C8C2×C4×D4312yes—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—432no—
680C4⋊C4—862no—
681C4⋊C4—864no—
682C4⋊C4—862no—
683C4⋊C4—864no—
684C4⋊C4—864no—
685C4⋊C4—861no—
686C4⋊C4—861no—
687C4⋊C4—861no—
688C4⋊C4D4×D4312yes—
689C22⋊C4—24no—
690C22⋊C4—862no—
691C22⋊C4—862no—
692C22⋊C4—864no—
693C22⋊C4—1722no—
694C42—21no—
695C42—21no—
696C42—864no—
697C42—864no—
698C42—861no—
699C42—861no—
700C42—1722no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—432no—
709C23—432no—
710C23—432no—
711C23—861no—
712C23—861no—
713C23—861no—
714C23—861no—
715C23C2×D4×D4311yescharacteristic
716Q8—22no—
717Q8—22no—
718Q8—41no—
719Q8—41no—
720Q8—434no—
721Q8—862no—
722Q8—862no—
723Q8—862no—
724Q8—862no—
725Q8—862no—
726Q8—1728no—
727Q8—1721no—
728Q8—1721no—
729D4—22no—
730D4—22no—
731D4—22no—
732D4—8616no—
733D4C22⋊C4×D4314yes—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—84no—
750C2×C4—432no—
751C2×C4—432no—
752C2×C4—432no—
753C2×C4—434no—
754C2×C4—434no—
755C2×C4—434no—
756C2×C4—434no—
757C2×C4—8616no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—861no—
763C2×C4—862no—
764C2×C4—861no—
765C2×C4—861no—
766C2×C4—861no—
767C2×C4—861no—
768C2×C4—861no—
769C2×C4—3444no—
770C2×C4—3444no—
771C2×C4—1728no—
772C2×C4—1721no—
773C2×C4—1721no—
774C2×C4—1721no—
775C2×C4—1721no—
776C2×C4—1721no—
777C2×C4—1721no—
778C2×C4—1721no—
779C2×C4C22×C4×D4311yescharacteristic
780C2×C4C2×D4×D4311yescharacteristic
781C2×C4C2×D4×D4311yescharacteristic
782C2×C4C2×D4×D4311yescharacteristic
783C2×C4#41×D4311yescharacteristic
784C2×C4#41×D4311yescharacteristic
785C8—22no—
786C8—41no—
787C8—862no—
788C8—1721no—
789C22—24no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—434no—
797C22—862no—
798C22—862no—
799C22—862no—
800C22—862no—
801C22—862no—
802C22—862no—
803C22C4×D4×D4311yescharacteristic
804C22#120×D4311yescharacteristic
805C22#121×D4311yescharacteristic
806C22#1458370511yescharacteristic
807C22#1458370911yescharacteristic
808C22#1458371311yescharacteristic
809C22#1458371511yescharacteristic
810C4—41no—
811C4—42no—
812C4—41no—
813C4—42no—
814C4—81no—
815C4—434no—
816C4—864no—
817C4—3441no—
818C4—1721no—
819C4—1722no—
820C4—1721no—
821C4—1722no—
822C4C2×C22⋊C4×D4311yescharacteristic
823C4C4×D4×D4311yescharacteristic
824C4#121×D4311yescharacteristic
825C4#123×D4311yescharacteristic
826C2—44no—
827C2—864no—
828C2#386×D4311yescharacteristic
829C2#1914343111yescharacteristic
830C2#1914343511yescharacteristic
831C2#1914386711yescharacteristic
832C2#1914388711yescharacteristic
833C2#1914414011yescharacteristic
834C2#1914414611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1877C2
socleC23×C43C22×D4
prime radicalC22×#10621900C22
cosocleC22×C4×C43C24
hypercenter#1877D43
hypocenterC43#20931
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1877

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. C2×#103×D43C2semidirect
5. #19137178C2semidirect
6. #19134939C2semidirect
7. #19134937C2semidirect
8. #19134935C2semidirect
9. #19134933C2semidirect
10. #19134931C2semidirect
11. #19134929C2semidirect
12. #19134927C2semidirect
13. #19134313C2semidirect
14. #19134290C2semidirect
15. C43×#1877C2semidirect
20. C2×#13063354C4semidirect
80. C2×Q8×D43C2×C4semidirect
90. C2×Dic172C2×C4semidirect
93. C2×#10621885C2×C4semidirect
96. C2×#10621883C2×C4semidirect
99. C2×#10621872C2×C4semidirect
153. C2×SD16×C43C2×C4semidirect
421. #1877D43semidirect
483. C43#20931semidirect
520. C2×SD16C4×D43semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#130633542
C2×#145833782
C2×#145828922
C2×#103×D432
#191371782
#191349392
#191349372
#191349352
#191349332
#191349312
#191349292
#191349272
#191343132
#191342902
C43×#18772
#2093143